On the use of higher-order azimuthal schemes in 3-D PE modeling

Journal of the Acoustical Society of America

Volumn 113, Issue 6, 2003, Pages 3134-3145

  Sturm, Frédéric ^a   Fawcett, John A ^b  

^a UNIVERSITÉ DE LYON   (France)

^b DEFENCE RESEARCH AND DEVELOPMENT CANADA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; FAST FOURIER TRANSFORMS; FINITE DIFFERENCE METHOD;

AZIMUTHAL SCHEMES;

ACOUSTIC WAVES;

ACOUSTICS;

ACCURACY; ACOUSTICS; ALGORITHM; ARTICLE; COMPUTER SIMULATION; ENERGY; FOURIER TRANSFORMATION; MODEL; PRESSURE; PRIORITY JOURNAL; SEA; SOUND;

EID: 0038282799     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.1572138     Document Type: Article

References (35)

1. C. F. Chen, J.-T. Lin, and D. Lee, "Acoustic three-dimensional effects around Taiwan strait: computational results," J. Comput. Acoust. 7, 15-26 (1999).
2. G. B. Deane, "The penetrable wedge as a three-dimensional benchmark," J. Acoust. Soc. Am. 103, 2989 (1998).
3. S. A. Glegg, G. B. Deane, and I. G. House, "Comparison between theory and model scale measurements of the three-dimensional sound propagation in a shear supporting penetrable wedge," J. Acoust. Soc. Am. 94, 2334-2342 (1993).
4. A. Tolstoy, "3-D propagation issues and models," J. Comput. Acoust. 4, 243-271 (1996).
5. D. Lee, A. D. Pierce, and E.-C. Shang, "Parabolic equation development in recent twentieth century," J. Comput. Acoust. 8, 527-637 (2000).
6. F. Sturm, M.-C. Pélissier, and D. Fattaccioli, "3D Sound propagation modelling with TRIPARADIM," in Proceedings of the 3rd European Conference on Underwater Acoustics, Heraklion, Crete, Greece (1996), pp. 243-248.
7. M. H. Schultz, D. Lee, and K. R. Jackson, "Application of the YALE sparse technique to solve three-dimensional parabolic wave equation," J. Acoust. Soc. Am. Suppl. 1 78, S96 (1983).
8. D. Lee, G. Botseas, and W. L. Siegmann, "Examination of three-dimensional effects using a propagation model with azimuth-coupling capability (FOR3D)," J. Acoust. Soc. Am. 91, 3192-3202 (1992).
9. M. D. Collins and S. A. Ching-Bing, "A three-dimensional parabolic equation model that includes the effects of rough boundaries," J. Acoust. Soc. Am. 87, 1104-1109 (1990).
10. J. A. Fawcett, "Modeling three-dimensional propagation in an oceanic wedge using parabolic equation methods," J. Acoust. Soc. Am. 93, 2627-2632 (1993).
11. K. B. Smith, "A three-dimensional propagation algorithm using finite azimuthal aperture," J. Acoust. Soc. Am. 106, 3231-3239 (1999).
12. F. Sturm, "Mise en évidence et analyse d'effets tridimensionnels par utilisation et confrontation de modles paraboliques 3D," (in French) in Proc. 4émes Journées d'études Acoustique Sous-Marine, Brest, France (1998), pp. 1-10.
13. G. H. Brooke, D. J. Thomson, and G. R. Ebbeson, "PECan: A Canadian Parabolic Equation Model for Underwater Sound Propagation," J. Comput. Acoust. 9, 69-100 (2001).
14. W. L. Siegmann, G. A. Kriegsmann, and D. Lee, "A wide-angle three-dimensional parabolic wave equation," J. Acoust. Soc. Am. 78, 659-664 (1985).
15. A. Bamberger, B. Engquist, L. Halpern, and P. Joly, "Higher order paraxial wave equation approximations in heterogeneous media," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 48, 129-154 (1988).
16. J. I. Arvelo and A. P. Rosenberg, "Three-dimensional effects on sound propagation and matched-field processor," J. Comput. Acoust. 9, 17-39 (2001).
17. M. D. Collins and E. K. Westwood, "A higher order energy-conserving parabolic equation for range-dependent ocean depth, sound speed, and density," J. Acoust. Soc. Am. 89, 1068-1075 (1991).
18. F. B. Jensen, W. A. Kuperman, M. B. Porter, and H. Schmidt, Computational Ocean Acoustics, AIP Series in Modern Acoustics and Signal Processing (AIP, New York, 1994).
19. F. D. Tappert, "The parabolic approximation method," in Wave Propagation and Underwater Acoustics, edited by J. B. Keller and J. S. Papadakis, Lecture Notes in Physics, Vol. 70 (Springer, Berlin, 1977), pp. 224-287.
20. C. Bernardi and M.-C. Pélissier, "Spectral approximation of a Schrödinger type equation," Math. Models Methods Appl. Sci. 4, 49-88 (1994).
21. F. Tappert and G. Brown, "Asymptotic phase error in parabolic approximations to the one-way Helmholtz equation," J. Acoust. Soc. Am. 99, 1405-1413 (1996).
22. F. Tappert, J. L. Spiesberger, and L. Boden, "New full-wave approximation for ocean acoustic travel time predictions," J. Acoust. Soc. Am. 97, 2771-2782 (1995).
23. F. Sturm and J. A. Fawcett, "Numerical simulation of the effects of the bathymetry on underwater sound propagation using three-dimensional parabolic equation models," SM-342 SACLANT Undersea Research Centre, La Spezia, Italy (1998).
24. H. Weinberg and R. Burridge, "Horizontal ray-theory for ocean acoustics," J. Acoust. Soc. Am. 55, 63-79 (1974).
25. F. Sturm, J. A. Fawcett, and F. B. Jensen, "Benchmarking two three-dimensional parabolic equation methods," J. Acoust. Soc. Am. 103, 2990 (1998).
26. R. B. Evans, "A coupled mode solution for acoustic propagation in a waveguide with stepwise depth variations of a penetrable bottom," J. Acoust. Soc. Am. 74, 188-195 (1983).
27. F. Jensen and C. M. Ferla, "Numerical solutions of range-dependent benchmark problems in ocean acoustics," J. Acoust. Soc. Am. 87, 1499-1510 (1990).
28. M. B. Porter, F. B. Jensen, and C. M. Ferla, "The problem of energy conservation on one way models," J. Acoust. Soc. Am. 89, 1058-1067 (1991).
29. G. H. Brooke, D. J. Thomson, and P. M. Wort, "A sloping boundary condition for efficient PE calculations in range-dependent acoustic media," J. Comput. Acoust. 4, 11-27 (1996).
30. M. D. Collins and R. B. Evans, "A two way parabolic equation for acoustic backscattering in the ocean," J. Acoust. Soc. Am. 91, 1357-1368 (1992).
31. N. A. Kampanis and E. T. Flouri, "On an energy conserving treatment of variable interfaces in a finite difference PE code," Acust. Acta Acust. 85, 18-23 (1999).
32. G. H. Brooke and D. J. Thomson, "A single-scatter formalism for improving PE calculations in range-dependent media," in NRL PE WORKSHOP II (Proceedings of the second parabolic equation workshop), edited by S. A. Chin-Bing, D. B. King, J. A. Davies, and R. B. Evans (Naval Research Laboratory, 1993), pp. 126-144.
33. M. J. Buckingham, "Theory of three-dimensional acoustic propagation in a wedgelike ocean with a penetrable bottom," J. Acoust. Soc. Am. 82, 198-210 (1987).
34. R. Doolittle, A. Tolstoy, and M. J. Buckingham, "Experimental confirmation of horizontal refraction of cw acoustic radiation from a point source in a wedge-shaped ocean environment," J. Acoust. Soc. Am. 83, 2117-2125 (1988).
35. G. B. Deane and M. J. Buckingham, "An analysis of the three-dimensional sound field in a penetrable wedge with a stratified fluid or elastic basement," J. Acoust. Soc. Am. 93, 1319-1328 (1993).